Kissing number for $\mathbb{R}^{12}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{12}$.
Lower bound:
$841$
Upper bound:
$1355$
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$756$
Checked construction
kissing-number-12-lower-756, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
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Lower bound: $840$
Reference unknown
[via Kissing number - Wikipedia] -
2022-02-24
Upper bound: $1355$
N. Leijenhorst and D. de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, Mathematical Programming Computation 16 (2024) 503-534, arXiv:2202.12077.
[via Kissing numbers, Henry Cohn] -
2026-06-17
Lower bound: $841$
R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in R^12 and a place for the 841st sphere, arXiv:2606.18984.
[via Kissing numbers, Henry Cohn]